1. Lecture 8 Review: Mesh Analysis Related educational materials:
Nodal analysis
Supernodes
Additional nodal analysis examples
Mesh Analysis
Related educational materials:
Chapter 3.2, 3.3

2. Review: Nodal Analysis
Choose reference node
Identify independent nodes
Label “constrained” voltages
Apply KCL at independent nodes
Write the KCL equations in terms of node voltages
Solve equations to determine the node voltages
Determine desired circuit parameters from node voltages

3. Supernodes
In example 3 of lecture 7, we applied KCL at a supernode

4. Supernodes – continued
Example:
A node is defined as having a single, unique voltage
We can, however, apply KCL at supernodes which contain multiple nodes

5. Supernodes in nodal analysis
Supernodes are especially useful in nodal analysis when dependent nodes (voltage sources) are present
Define a supernode containing the dependent nodes
The supernode contains the voltage source and the nodes to which it is connected
Apply KCL at the supernode

6. Supernodes are useful, but not required
Supernodes are not essential for nodal analysis, as long as you account for all currents
Need to explicitly include currents through voltage sources
Lecture 7, Example 3:

7. Lecture 7, Example 3 – alternate approach

8. Example 1
Determine the voltage across the 6 resistor

9. Example 1 – alternate approach

10. Example 2
Use nodal analysis to write a set of equations from which you can determine the current through the 6 resistor.

11. Mesh analysis – review Identify mesh loops
The currents around these loops are the mesh currents
Use Ohm’s Law to write KVL around each loop in terms of the mesh currents
Solve these equations to determine the mesh currents
Any desired circuit parameter can be determined from the mesh currents

12. Nodal and mesh analysis – comparison
Nodal analysis:
Define independent nodes
Apply KCL at independent nodes
Use Ohm’s Law to write KCL in terms of node voltages
Mesh analysis:
Define “mesh loops”
Apply KVL around the mesh loops
Use Ohm’s Law to write KVL in terms of mesh currents

13. Mesh Analysis
We will illustrate the mesh analysis technique in the context of an example circuit:

14. Mesh Analysis Step 1: Choose mesh loops and identify mesh currents
Kill sources (short voltage sources, open-circuit current sources)
Recommendation: mesh loops should not have other loops in their interior

15. Mesh Analysis Step 2: Replace sources and write constrained loops
Constrained loops go through current sources
Constrained loops are somewhat arbitrary, but their direction and magnitude must be consistent with the source through which they pass

16. Mesh Analysis Step 3: Apply KVL around the mesh loops
Use Ohm’s Law to write voltage drops in terms of mesh currents
Voltage polarities in KVL must be consistent with that loop’s mesh current

17. Mesh Analysis
Step 3: continued

18. Mesh Analysis Step 4: Solve the equations for mesh currents
Use mesh currents to determine the circuit parameters of interest
Note: The total current in an element is the sum of the mesh currents in the element